Pimskeks of the Evad3rs Dev-Team reveals that those looking to apply the new iOS 6.1 jailbreak should update to the firmware using iTunes.

If you people plan to upgrade to iOS 6.1 please don't do an OTA upgrade. Please make a full restore using iTunes.

Just moments ago Planetbeing confirmed that their untethered jailbreak works with new iOS 6.1 final firmware released by Apple today and MuscleNerd hinted that the jailbreak will be released this Sunday.

Update:
MuscleNerd offers some insight as to why this is necessary, "a few reasons: OTA is more time consuming for us to test, and it gives you different SHSH blobs than normal restore."

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My 2 cents... Download the firmware from iClarified and then use Shift+Update (I think it's shift? It's been a while..?) in iTunes to update your device. The firmware will download super fast (I got the 900MB file in 2 minutes) and you can be satisfied that you have the .ipsw sitting on your PC at a known location. Very handy if the update goes wonky in iTunes or if there is a mass of iTunes users trying to do it at the same time.